6x(5x+8)=-6

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Solution for 6x(5x+8)=-6 equation: 


Simplifying
6x(5x + 8) = -6

Reorder the terms:
6x(8 + 5x) = -6
(8 * 6x + 5x * 6x) = -6
(48x + 30x2) = -6

Solving
48x + 30x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 48x + 30x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 48x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 8x + 5x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + 8x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + 8x + 5x2 = 0

Solving
1 + 8x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.2 + 1.6x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.6x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.6x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.6x + x2 = 0 + -0.2
1.6x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.6x + x2 = -0.2

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = -0.2 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = -0.2 + 0.64

Combine like terms: -0.2 + 0.64 = 0.44
0.64 + 1.6x + x2 = 0.44

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(x + 0.8) equal to 0.663324958 and -0.663324958.


Subproblem 1
x + 0.8 = 0.663324958

Simplifying
x + 0.8 = 0.663324958

Reorder the terms:
0.8 + x = 0.663324958

Solving
0.8 + x = 0.663324958

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 0.663324958 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 0.663324958 + -0.8
x = 0.663324958 + -0.8

Combine like terms: 0.663324958 + -0.8 = -0.136675042
x = -0.136675042

Simplifying
x = -0.136675042


Subproblem 2
x + 0.8 = -0.663324958

Simplifying
x + 0.8 = -0.663324958

Reorder the terms:
0.8 + x = -0.663324958

Solving
0.8 + x = -0.663324958

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -0.663324958 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -0.663324958 + -0.8
x = -0.663324958 + -0.8

Combine like terms: -0.663324958 + -0.8 = -1.463324958
x = -1.463324958

Simplifying
x = -1.463324958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.136675042, -1.463324958}
Solution
x = {-0.136675042, -1.463324958}

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